{"title":"稳定性和等变格罗莫夫-豪斯多夫收敛性","authors":"Mohammad Alattar","doi":"10.1112/blms.13073","DOIUrl":null,"url":null,"abstract":"<p>We give applications of equivariant Gromov–Hausdorff convergence in various contexts. Namely, using equivariant Gromov–Hausdorff convergence, we prove a stability result in the setting of compact finite-dimensional Alexandrov spaces. Moreover, we introduce the notion of an <i>almost commutative diagram</i> and show that its use simplifies both exposition and argument.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 8","pages":"2585-2596"},"PeriodicalIF":0.8000,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13073","citationCount":"0","resultStr":"{\"title\":\"Stability and equivariant Gromov–Hausdorff convergence\",\"authors\":\"Mohammad Alattar\",\"doi\":\"10.1112/blms.13073\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We give applications of equivariant Gromov–Hausdorff convergence in various contexts. Namely, using equivariant Gromov–Hausdorff convergence, we prove a stability result in the setting of compact finite-dimensional Alexandrov spaces. Moreover, we introduce the notion of an <i>almost commutative diagram</i> and show that its use simplifies both exposition and argument.</p>\",\"PeriodicalId\":55298,\"journal\":{\"name\":\"Bulletin of the London Mathematical Society\",\"volume\":\"56 8\",\"pages\":\"2585-2596\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-05-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13073\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the London Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/blms.13073\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the London Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/blms.13073","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Stability and equivariant Gromov–Hausdorff convergence
We give applications of equivariant Gromov–Hausdorff convergence in various contexts. Namely, using equivariant Gromov–Hausdorff convergence, we prove a stability result in the setting of compact finite-dimensional Alexandrov spaces. Moreover, we introduce the notion of an almost commutative diagram and show that its use simplifies both exposition and argument.
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